Critical collapse of the exchange-enhanced spin splitting in two-dimensional systems

The critical filling factor νc where Shubnikov--de Haas oscillations become spin split is investigated for a set of GaAs-GaₓAl_1-xAs heterojunctions. Finite-temperature magnetoresistance measurements are used to extract the value of νc at zero temperature. The critical point is where the disorder potential has the same magnitude as the exchange energy, leading to the empirical relationship νc=g*nₑτₛh/2m₀. This is valid for all the samples studied, where the density nₑ and single particle lifetime τₛ both vary by more than an order of magnitude, and g* the exchange-enhanced g factor has a weak dependence on density. For each sample the spin-gap energy shows a linear increase with the magnetic field. Experiments in the tilted magnetic field show the spin gap is the sum of the bare Zeeman energy and an exchange term. This explains why measurements of the enhanced g factor from activation energy studies in the perpendicular field and the coincidence method in tilted fields have previously disagreed.